We remark that [1]}, [2]} have shown (see [2]}) how to take an LTC with rate arbitrarily close to 1 and with constant distance, and construct a new LTC with rate and distance approaching the Gilbert-Varshamov bound, and only a constant overhead in the locality \(q\) . So the theorem above holds for all \(r,\delta >0\)  that satisfy \(r+h(\delta )<1\)  where \(h(\cdot )\)  is the binary entropy function.
